The Calculation of Turning Points of Nonlinear Equations

The Calculation of Turning Points of Nonlinear Equations
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非线性方程转折点的计算

DOI：
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发表时间：
1980
期刊：
影响因子：
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通讯作者：
A. Spence
A. Spence
中科院分区：
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文献类型：
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作者：
G. Moore;A. Spence

文献摘要

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本文研究了一类含参数非线性方程的奇点的判定问题，称之为“转折点”或“极限点”。引入了一个扩大的系统，其转向点是一个非奇异的解决方案，因此可以使用标准的方法来计算它。一个有效的实施牛顿法在有限维的情况下，并给出数值结果离散的微分方程和积分方程。
This paper is concerned with the determination of a type of singular point, called a “turning” or “limit” point, of nonlinear equations depending on a parameter. An enlarged system is introduced for which the turning point is a nonsingular solution and thus standard methods can be used to compute it. An efficient implementation of Newton’s method in the finite-dimensional case is presented and numerical results for discretizations of a differential equation and an integral equation are given.